Electronic squaring circuit



May 11, 1M8. F, BERGER E rm. 2,441,387

" smc'momc squmms cmcun' Filed Oct. 30,1944

PLATE CURRENT GRID VOLTAGE FIG.3. r.

TO CONDENSER 7|, AND mom: 13,

FIG.3.

INVENTOR.

v FRANCE 8. BERGER .BY WILLIAM A. HIGINBOTHAM Patented May 11, 1948ELECTRONIC SQUARING CIRCUIT France B. Berger, Watertown, Mass, andWilliam A. Higinbotham, Santa Fe., N. Mex., assignors, by mesneassignments, to the United States of America as represented by theSecretary of War.

Application October 30, 1944, Serial No. 561,021

3 Claims. (Cl. 25027) This invention relates to electrical means forproducing an output voltage or current which is a given function of aninput voltage or current,

and it relates more particularly to electrical Another object of thepresent invention is to have the output of this circuit respondpractically simultaneously with any changes in the input, which is ofparticular value in connection with sweep circuits of cathode ray tubes.

Still anotherobject of the present invention is to provide a simple, yethighly accurate and reliable, circuit to achieve the above-mentionedobjects. I

The above and other objects in view will appear more fully from thefollowing detailed description, accompanying drawings and appendedclaims. r

Referring now to the drawing wherein:

Fig. 1 is a simplified diagram of one specific embodiment of the presentinvention;

Fig, 2 is a graph showing variation of plate current (i vs. grid voltage(e for each of the tubes shown in the diagram of Fig. 1, with the sum ofthe plate currents being represented by the dashed curve;

Fig. 3 represents a schematic diagram of an illustrative embodiment ofthe present invention for which Fig. l is the simplified Versionthereof; and

Fig. 4 is a schematic diagram illustrating modified connections of Fig.3.

It is to be understood that the circuit represented generally by Fig, 1and more specifically by Fig. 3 may be referred to as a "squaringcircuit.

Referring now to Fig. 1, the input signal to the 2 squaring circuitis'applied between terminal 5 and grounded terminal 6. The input maythen be fed through biasing means 1 to control grid 8 of vacuum tube 9.At the same time, the input may be fed through a phase inverter In, theoutput being a voltage substantially the same as that applied to controlgrid 8 of vacuum tube 9 but being out of phase therewith. This voltagemay then be fed through biasing means II to control grid l2 of vacuumtube l3. Voltages appearing on control grid 8 of vacuum tube 9 andcontrol grid l2 of vacuum tube l3 are then substantially equal but ofopposite polarity. Cathode'l5 of vacuum tube 9 and cathode [6 of vacuumtube l3 may be connected to ground, and anode ll of vacuum tube 9 andanode [8 of vacuum tube l3 may be connected together and thence througha common load impedance 2!! to a source of 3+ potential 2!. The cathodesand anodes of tubes 9 and I3 are thus connected in a commoncathode-anode circuit. I

The general expression for plate current in a vacuum tube may beexpressed as where a: is the voltage applied to the control grid, wherea, b, c and d depend upon the particular characteristics of the vacuumtube. If the tubes are operated entirely within the negative gridvoltage region, fourth and higher powers of this series may beneglected. The general expression for plate current in vacuum tube I3may be expressed as aba:+cx d:r the change in sign of a: being due tothefact that the voltage appearing at control grid l2 of vacuum tube 13although similar to that applied to control grid 8 of vacuum tube 9, isof opposite polarity.

' The-plate currents for vacuum tube 9 and vacuum tube 13 will flowthrough common load impedance 20. By addition of the two expressions forplate current, and neglecting terms above the third power, it will beseen that the odd power terms cancel out, leaving the resultantexpression 2a+2cx 2a being a constant which can be eliminated bysuitable level-setting action and 20 being a proportionality factorwhich can be altered, if desired, by suitable amplification orattenunation. Since the voltage output in question is that produced bythe flow of the plate currents of vacuum tubes 9 and I3 through loadimpedance 2B, the voltage output will vary as the term x thus providingthe squaring feature of the present invention.

A graphical representation of the plate currents for vacuum tubes 9 andI3 is given in Fig, 2. The curve 7:13 may represent the mutualcharacteristic curve of vacuum tube 9, and is plotted in the normalsense where the origin of the curve is at the lower right-hand cornerand, the plate current i increases with an increase of grid voltage reto the, right. The curve 21 similarly may represent; the plate currentof? vacuum tube i3, and is drawn to the same ordinate scale as curve ipbut with the abscissa in the opposite direction, that is to say platecurrent i increases as grid voltage e increases to the left,.the,0ri1-gin of this curve being at the. lower left-hand corner. The dashed curveshown. in Fig..2,.obtained by adding the ordinatesof? i and. ip and thusrepresenting the resultant: plate current through load impedance 20, isvery nearly that of a parabola; or in other words, varies as a squaredfunction.

The characteristic curves shown in Fig. 2; are

merely representative of plate current vs. grid voltage curves, andmay,typify the operation of varioustypes of vacuum tubes... For ease ofdescription, certain Voltageswhi'ch may. be realized in. actualoperation. have been. indicated. directly on these curves. These/arevnot. to. be construed as required voltages to. be applied to. thecircuit, but merely represent valuesthat have been .found suitable inone illustrative embodiment. of the present invention (Fig. 3.). wherein638 type vacuum' tubes are used. in. place, of; vacuum. tubes; 9 and:l3-of- Fig. l. The.-6B8. type tube was found to have particularlysuitable characteristics for the purposes of. the present. invention,due. in large measure: to. the. high, second harmonic. dis.- tortion.produced by. tubes oh that type- CIther tubes having similar.characteristics. might-also beusedifor this purpose.

Referring nowto Fig-2,- it will. be. noted that the characteristiccurves of plate current. vs. grid voltageintersect at pointZZ, whiohishereinafter referred to as; the. crossover point This point willgenerally, because. of the symmetry of the figure, intersect the. ridvoltage axis half. way between the origins of the two graphs. Thecrossover point repr-esents the value of grid voltage at which theresulting plate current flowing through load, impedance 2!! of Fig. 1willbe at its. minimum. This therefore may represent the point at. whichthesi'gnal input at terminal 5-of Fig. 1 is zero. If" then the signalapplied to terminal 5' is, increased in;a.positive-direction; the platecurrent. ip of vacuum tube '9 will-increase, and at the same time,platecurrent zp of vacuum tubeltlwill. decrease. If, however, the.signal-applied-to terminal 5 is,.increased in' a negative direction, theplate currenti of" vacuum tube: l3 will: increase and at. thesame. time.plate current ip' or vacuum. tube. 9. will. decrease. As previouslymentioned, the opposite acti'ons of vac.- uumtubes. El and. i3 are dueto. the fact thatthe signals appearing; on. the control. grids of. thesetubes: are. of opposite. polarity/ The resultant current flowingthrough: load impedance 2b. of Fig,- 1 is thB'SumOfip and i11 andisrepresented by the; dotted: curve of- Fig. 2 which;issubstantiallyparabolic in form.

Anychange inthe input signalionz terminal 5; from Y the. value Icorresponding to the crossover point; will'prcduce a changeinthe voltageacross load impedance: 20 proportionalatothe-square of 4 the change inthe input signal. Thus the input signal applied to terminal 5 may beeither negative-going or positive-going. It is preferable for the inputsignal to begin at a value corresponding to the crossover point, saidpoint coinciding with minimum current flow through load impedance 2b andhence maximum voltage output.

Referring now to the embodiment shown in Fig. 3, vacuum tubes 3c and filthereof correspond to vacuum tubes 9 and H of the simplifiedversionshown in Fig. 1.. The. particular tubes 39 and 3| may be pentodesoffthe 638 type, it being understood, of course, that other tubes havingsimilar characteristics may be used. Vacuum tube 32 acts as an amplifierand phase inverter. Vacuum tube also acts as an amplifier wherein thesignalinput isapplied to cathode M, the outputat. anode 58 being of thesame phase as the input. to. cathode 4|. Tubes 32 and 33 to getherprovide essentially the phase-inverting action required of the inverterl0 shown in Fig. l. The type of tubes which may be used here is notparticularly critical, but may be of the medium-mu-yarietv'such as a6SN'7, or of the high mu variety, such as the 6SL7. Inasmuch as theseparticular. tube. types. have. two triode elements in a-singl'e.envelope, theyare particularly suitableforuse inthepresent invention.

Whenthesignalinput is appliedto t'ermi'nalS' I a voltagawhich isdevelopedacross grid leak.resister 35' connected to ground, is appliedto con.- trol grid 36. of vacuumtube 32. One voltage outputisdeveloped'across anode. load resistor. 5 l and is applied directly to.controllgrid 38" of vacuum tube 39, and a second outputis.developed'across variable: cathode load resistorv 41 and is. applieddirectly'to cathode 4-1 ofivacuum. tube 331. Variable cathode resistor4Z.has one-sideconnectedlto cathodes All and 41 ofvacuumitubesfll-and,33', and. the. other sideconnected to'a negative. voltage: bias source.43,. the positive. side.v of the latter being connectedz to ground.

By means of variable resistance; 42,.the:volt.- age drop: across: loadresistance iifl may be. adjustedin order to obtain thadesirediinitialvoltage output at junction. 6|. This; variable. resistance may be. oneof the. conventional type or maybe a pentodety-pevacuum tubehavingtheadvantage of substantially constant. currentfi'ow-..

The potentialof control.- grid 44 of: vacuum tube 33- may be variedpositively or negatively with respect to ground by means ofpotentiometer 45, the arm ofwhich is connected to-said grid. Oneside ofpotentiometer 45-is connected to the positive terminal'of biasingmeans'46; the'negae tive terminal being connected to ground.v The other sideof potentiometer 45'is connected to the negative' terminal: of; biasingmeans; 41, the positive terminal being: connected to ground. Thethus-achieved variation of potentialion: control' grid 44 serves: ineffect: relatively to; shift the characteristic curves of the: pentodes,thus embodiment shown in-Fig.- 3, is potential source 62.

The signals issuing from -anode 50 of vacuum tube 33 and anode31 ofvacuum tube 32 are 180 out of phase with respect to each other. Thesignal issuing'from anode 31 may be fed directly to control. grid 38 ofvacuum tube 30, and the signal issuing from;anode; 50'may be feddirectly to control grid 53 of vacuum tube 3|. Due to the fact that theoutputs at the anodes of vacuum tubes 32 .and 33 are coupled directly tovacuum tubes 30 andi3l, respectively, the latter are operated at ahigher voltage level than vacuum tubes 32 and 33. For this reason, inthe embodiment shown, cathodes 55 and 56 of vacuum tubes 30 and 3| areconnected together and thence to a source of positive potential 61.

An advantage of the direct coupling between tubes 33 and 3|, and between32 and 30, is that objectionable time constants are obviated thereby,thus enabling the circuit to respond almost instantaneously to changesin the original input on terminal 34.

Suppressor grids 65 and 66 of vacuum tubes 30 and 3| may be connected totheir respective cathodes 55 and 55. Anodes 51 and 58 of vacuum tubes 30and 3|, respectively, are also connected together and thence to a sourceof B potential 69 through load resistance 60. The plate currents ofvacuum tubes 30 and 3| are combined in load resistance 60, the resultantcurrent varying as the square of the input signal to terminal 34.However, the voltage drop across load resistance 5D varies negatively asthe square of the input to terminal 34. The output of the foregoingsquaring circuit may be taken directly from the anodes 51 and 58 atjunction 6|.

If vacuum tubes 32 and 33 are either GSN'Is or 6SL7s and vacuum tubes 30and 3| are 6B8s, the following voltages have been found to be quitesuitable in the embodiment shown in Fig. 3. Voltage source 43, whichprovides negative bias for cathodes 49 and 4| of vacuum tubes 32 and 33,respectively, may be approximately 150 volts. Positive potential source62 may be approximately 200 volts, and positive potential source 39 maybe approximately 350 volts, and positive potential source 61, whichsupplies bias for cathodes 55 and 53, may be approximately 100 volts.

If 6B8s are used, the crossover'point (Fig. 2) will occur at a gridvoltage of approximately -12 Volts. This means that when the signalinput to the squaring circuit is zero, variable resistance 52 can beadjusted so that control grids 3B and 53 of vacuum tubes 30 and 3|,respectively, are about I2 volts below the potential of their cathodes55 and 56.

Under these conditions the resultant current (represented by the dashedcurve of Fig. 2) will remain substantially parabolic for a signal inputvariation of about 16 volts.

The voltage output from junction point 6| of Fig. 3, which variesnegatively as the square of the input voltage to terminal 34, thereforevaries with respect to the relatively high D.-C. potential at junctionpoint 6| by a factor proportional to the square of the signal inputvoltage. It may be desirable, however, to obtain a voltage which variesfrom ground potential by the aforesaid factor. This may be accomplishedby the use of a relatively simple level-setting circuit, which isindicated by the dashed portion of Fig. 3. This circuit is usuallyreferred to as a D.-C. restorer 'or clamping circui and is well knowninthe art.

The D.-C. restorer or clamping circuit-may comprise condenser II,resistor 12; vacuum tube 13, and output terminals Hiand 15. For generaloperation, the time constant'determined by the values of condenser H andresistor 12 should be large as compared to the period-of the inputvoltage to terminal 34. The voltage output of the D.-C. restorer orclampingcircuit is taken from anode 16 of vacuum tube 13 and'variesnegatively with respect to ground as the square of the voltage appliedto terminal 34. p

Although the discussion of the basic operation of the circuit of Fig. 1indicated that the variable input is applied to the grids of vacuumtubes 9 and I3, if desired, in other embodiments the input may beapplied to the cathodes and the grids connected to ground as illustratedin Fig. 4. The connections in Fig. 4 are identical to those illustratedin Fig. 3, except that the cathodes 55 and 5B of the pentodes 30 and 3|are now connected to the plates of the triodes 32 and 33 and the controlgrids 38 and 53 are grounded through a biasing battery 61-11, the lattercorresponding in its function to the biasing battery 61 in Fig. 3.

Although separate vacuum tubes have been shown in the drawings, it is tobe understood that, if desired, their electrodes may be placed inside asingle envelope as in a multi-purpose tube.

One specific application of the present invention is shown in copendingapplication of Luis W. Alvarez, Serial No. 542,287, filed June 27, 1944,wherein it was desired to obtain a voltage that varied directly as thesquare of another voltage. Other applications of the invention may bemade in electrical calculating or computing machines whereinrepresentation of squared term functions are needed. These and otherapplications of the present invention will readily occur to thoseskilled in the art.

Having thus described the invention, what is hereby claimed as new anddesired to be protected by Letters Patent is:

1. A squaring circuit including vacuum tube means having a platecircuit, a grid circuit and a cathode circuit, at least one of thelatter two circuits including tWo separate electrode elements, means forapplying substantially similar input signals of opposite polarity tosaid electrode elements, and a load impedance in the plate circuit, theoutput developed across said load impedance being substantiallyproportional to the square of the input.

2. A squaring circuit including vacuum tube means having two separatecontrol grids and a common cathode-anode circuit, means for applying aninput signal to one of said control grids, inversion means for producinga substantially similar signal to opposite polarity, means for applyingsaid latter signal to the other one of said control grids, and a loadimpedanc in the cathode-anode circuit, the output developed across saidload impedance being substantially proportional to the square of theinput.

3. A squaring circuit including a pair of vac uum tubes each containingat least a cathode, an anode and a control grid, a common anodecathodecircuit for said tubes, another vacuum tube containing a cathode, ananode and a control grid and having anode and cathode load impedances,means for applying an input signal to the control grid of saidlast-mentioned tube,

marshy developingz signafls: air oppositei polarity across saidimpedances, means for applyingthe signalzkieve'lopedfacnoss the'anadeioa-da impedance t0ath-acontrohgridi of: one a ofzithe'itubes: ofsaid first lmenti'onedz pain'of; tubes;- and means for: anplyifi'g thesig-nalildeveloped aaross =thecathode ldaw-impedance to thiicontrol":gridzof the other tube-of said paimofftubes; saidrg-ridiappliedsignalsmf opposite' polarity being-substantially:simi,lssiria-nd aslbadfiimpedance in th'e common anodecathod circuit of saidfirst-mentioned" pair of tflb'es: the" outputbeing: de'velbped acrosssaid. last-mentioned "162x]. impedance and being substantiallyr:promrtionahtmthesqua'zze oiltheainnut signal.

FRANGE; B. BERGER.

A. I-IIGHV-BOTHAMI;

REEERENQES; CITED.

Theifollowing-zreferences:arewf record!in the file ofthis patent:

UNITED p STATEST PATENTS Number Name Date;- 7

12728 311 Taylor Sept: 1.7; 1.929 2,199,820 Gannett May 7; 19.40

